Overflow use case:

Create a new queue at 'My Settings' > 'Queues' that you could call "Overflow Queue". Add the new agent to the queue. The queue selection would be very simple: just always call the "Overflow Agent" in our example. You can of course add as many overflow agents as you want.

This overflow service queue can now be used in any call flow application in order to route with trigger-based conditions for business hours, holiday or availability. E.g., you could forward calls to your overflow queue if all your agents in your main queue are busy. Or you could forward calls to the overflow queue if the call wasn't answered within a certain time frame. In other words, you can use the overflow agent instead of a callback request or voicemail.

Working with priorities:

Add the overflow agent to the main call queue but make sure to set up a prioritization, e.g. the overflow agent could be the last to take the call if none of your internal agents were available. This can be achieved by adding tags or creating a new group. Find more details for prioritizing calls here.

Be aware, if you only add one overflow agent, your outsourcing partner will only be able to take one call at the time.